@article{Zaki2025,

title = {Turbulence from an Observer Perspective},

author = {Tamer A. Zaki},

doi = {10.1146/annurev-fluid-030424-114735},

issn = {1545-4479},

year  = {2025},

date = {2025-01-22},

volume = {57},

number = {1},

pages = {311--334},

publisher = {Annual Reviews},

abstract = {Turbulence is often studied by tracking its spatiotemporal evolution and analyzing the dynamics of its different scales. The dual to this perspective is that of an observer who starts from measurements, or observations, of turbulence and attempts to identify their back-in-time origin, which is the foundation of data assimilation. This back-in-time search must contend with the action of chaos, which obfuscates the interpretation of the observations. When the available measurements satisfy a critical resolution threshold, the influence of chaos can be entirely mitigated and turbulence can be synchronized to the exact state–space trajectory that generated the observations. The critical threshold offers a new interpretation of the Taylor microscale, one that underscores its causal influence. Below the critical threshold, the origin of measurements becomes less definitive in regions where the flow is inconsequential to the observations. In contrast, flow events that influence the measurements, or are within their domain of dependence, are accurately captured. The implications for our understanding of wall turbulence are explored, starting with the highest density of measurements that entirely tame chaos and proceeding all the way to an isolated measurement of wall stress. The article concludes with a discussion of future opportunities and a call to action.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Zaki2025b,

title = {Turbulence from an Observer Perspective},

author = {Tamer A. Zaki},

doi = {10.1146/annurev-fluid-030424-114735},

issn = {1545-4479},

year  = {2025},

date = {2025-01-22},

volume = {57},

number = {1},

pages = {311--334},

publisher = {Annual Reviews},

abstract = {Turbulence is often studied by tracking its spatiotemporal evolution and analyzing the dynamics of its different scales. The dual to this perspective is that of an observer who starts from measurements, or observations, of turbulence and attempts to identify their back-in-time origin, which is the foundation of data assimilation. This back-in-time search must contend with the action of chaos, which obfuscates the interpretation of the observations. When the available measurements satisfy a critical resolution threshold, the influence of chaos can be entirely mitigated and turbulence can be synchronized to the exact state–space trajectory that generated the observations. The critical threshold offers a new interpretation of the Taylor microscale, one that underscores its causal influence. Below the critical threshold, the origin of measurements becomes less definitive in regions where the flow is inconsequential to the observations. In contrast, flow events that influence the measurements, or are within their domain of dependence, are accurately captured. The implications for our understanding of wall turbulence are explored, starting with the highest density of measurements that entirely tame chaos and proceeding all the way to an isolated measurement of wall stress. The article concludes with a discussion of future opportunities and a call to action.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Toedtli2024,

title = {Localization of internal gravity waves in stratified channel flow},

author = {Simon S. Toedtli and Pierluigi Morra and Tamer A. Zaki},

doi = {10.1017/jfm.2024.836},

issn = {1469-7645},

year  = {2024},

date = {2024-11-25},

journal = {J. Fluid Mech.},

volume = {1000},

publisher = {Cambridge University Press (CUP)},

abstract = {Linear and nonlinear contributions to the localization and dynamics of internal gravity waves in a stably stratified turbulent channel flow are investigated using data from direct numerical simulations (DNS). The classification into linear and nonlinear mechanisms is based on the resolvent formulation of the Navier–Stokes equations, which interprets velocity and temperature fluctuations (flow response) as the result of a linear operator (resolvent) acting on the nonlinear advection terms (forcing). Spatial and spatio-temporal power spectral densities computed from DNS data demonstrate that the stratified flow response is localized in spectral space and in the channel core, while the nonlinear forcing is broadband and spans up to the entire channel height. The localization of the velocity and temperature fluctuations in wavenumber and frequency is captured by the leading singular value of the resolvent operator. The wall-normal localization on the other hand results from a combination of linear dynamics and nonlinear forcing, and the latter is further examined using the cross-spectral density (CSD) tensor. Wall-normal subsets of the forcing CSD lead to flow responses that reveal a three-layer structure. The middle one hosts the critical layer of the gravity wave, and is termed the outer layer since it is flanked by an inner layer at the wall and the core region at the channel centre. Forcing within this outer layer generates the majority of the flow response in the channel core. Furthermore, a decomposition of the forcing CSD into velocity and temperature demonstrates that each imprints distinct phase relations on their associated responses, which lead to destructive interference and localization of the gravity waves in the channel core.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Yao2024c,

title = {Comparing local energy cascade rates in isotropic turbulence using structure-function and filtering formulations},

author = {Hanxun Yao and Michael Schnaubelt and Alexander S. Szalay and Tamer A. Zaki and Charles Meneveau},

doi = {10.1017/jfm.2023.1066},

issn = {1469-7645},

year  = {2024},

date = {2024-02-06},

journal = {J. Fluid Mech.},

volume = {980},

publisher = {Cambridge University Press (CUP)},

abstract = {Two common definitions of the spatially local rate of kinetic energy cascade at some scale 

	      

		

		$ell$

	      

	     in turbulent flows are (i) the cubic velocity difference term appearing in the ‘scale-integrated local Kolmogorov–Hill’ equation (structure-function approach), and (ii) the subfilter-scale energy flux term in the transport equation for subgrid-scale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylor-scale Reynolds number 1250. While in the past observations of negative subfilter-scale energy flux (backscatter) have led to debates regarding interpretation and relevance of such observations, we argue that the interpretation of the local structure-function-based cascade rate definition is unambiguous since it arises from a divergence term in scale space. Conditional averaging is used to explore the relationship between the local cascade rate and the local filtered viscous dissipation rate as well as filtered velocity gradient tensor properties such as its invariants. We find statistically robust evidence of inverse cascade when both the large-scale rotation rate is strong and the large-scale strain rate is weak. Even stronger net inverse cascading is observed in the ‘vortex compression’ 

	      

		

		$R>0$

	      

	    , 

	      

		

		$Q>0$

	      

	     quadrant, where 

	      

		

		$R$

	      

	     and 

	      

		

		$Q$

	      

	     are velocity gradient invariants. Qualitatively similar but quantitatively much weaker trends are observed for the conditionally averaged subfilter-scale energy flux. Flow visualizations show consistent trends, namely that spatially, the inverse cascade events appear to be located within large-scale vortices, specifically in subregions when 

	      

		

		$R$

	      

	     is large.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Yao2024b,

title = {Comparing local energy cascade rates in isotropic turbulence using structure-function and filtering formulations},

author = {Hanxun Yao and Michael Schnaubelt and Alexander S. Szalay and Tamer A. Zaki and Charles Meneveau},

doi = {10.1017/jfm.2023.1066},

issn = {1469-7645},

year  = {2024},

date = {2024-02-06},

journal = {J. Fluid Mech.},

volume = {980},

publisher = {Cambridge University Press (CUP)},

abstract = {Two common definitions of the spatially local rate of kinetic energy cascade at some scale 

	      

		

		$ell$

	      

	     in turbulent flows are (i) the cubic velocity difference term appearing in the ‘scale-integrated local Kolmogorov–Hill’ equation (structure-function approach), and (ii) the subfilter-scale energy flux term in the transport equation for subgrid-scale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylor-scale Reynolds number 1250. While in the past observations of negative subfilter-scale energy flux (backscatter) have led to debates regarding interpretation and relevance of such observations, we argue that the interpretation of the local structure-function-based cascade rate definition is unambiguous since it arises from a divergence term in scale space. Conditional averaging is used to explore the relationship between the local cascade rate and the local filtered viscous dissipation rate as well as filtered velocity gradient tensor properties such as its invariants. We find statistically robust evidence of inverse cascade when both the large-scale rotation rate is strong and the large-scale strain rate is weak. Even stronger net inverse cascading is observed in the ‘vortex compression’ 

	      

		

		$R>0$

	      

	    , 

	      

		

		$Q>0$

	      

	     quadrant, where 

	      

		

		$R$

	      

	     and 

	      

		

		$Q$

	      

	     are velocity gradient invariants. Qualitatively similar but quantitatively much weaker trends are observed for the conditionally averaged subfilter-scale energy flux. Flow visualizations show consistent trends, namely that spatially, the inverse cascade events appear to be located within large-scale vortices, specifically in subregions when 

	      

		

		$R$

	      

	     is large.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Yao2024,

title = {Comparing local energy cascade rates in isotropic turbulence using structure-function and filtering formulations},

author = {Hanxun Yao and Michael Schnaubelt and Alexander S. Szalay and Tamer A. Zaki and Charles Meneveau},

doi = {10.1017/jfm.2023.1066},

issn = {1469-7645},

year  = {2024},

date = {2024-02-06},

journal = {J. Fluid Mech.},

volume = {980},

publisher = {Cambridge University Press (CUP)},

abstract = {Two common definitions of the spatially local rate of kinetic energy cascade at some scale 

	      

		

		$ell$

	      

	     in turbulent flows are (i) the cubic velocity difference term appearing in the ‘scale-integrated local Kolmogorov–Hill’ equation (structure-function approach), and (ii) the subfilter-scale energy flux term in the transport equation for subgrid-scale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylor-scale Reynolds number 1250. While in the past observations of negative subfilter-scale energy flux (backscatter) have led to debates regarding interpretation and relevance of such observations, we argue that the interpretation of the local structure-function-based cascade rate definition is unambiguous since it arises from a divergence term in scale space. Conditional averaging is used to explore the relationship between the local cascade rate and the local filtered viscous dissipation rate as well as filtered velocity gradient tensor properties such as its invariants. We find statistically robust evidence of inverse cascade when both the large-scale rotation rate is strong and the large-scale strain rate is weak. Even stronger net inverse cascading is observed in the ‘vortex compression’ 

	      

		

		$R>0$

	      

	    , 

	      

		

		$Q>0$

	      

	     quadrant, where 

	      

		

		$R$

	      

	     and 

	      

		

		$Q$

	      

	     are velocity gradient invariants. Qualitatively similar but quantitatively much weaker trends are observed for the conditionally averaged subfilter-scale energy flux. Flow visualizations show consistent trends, namely that spatially, the inverse cascade events appear to be located within large-scale vortices, specifically in subregions when 

	      

		

		$R$

	      

	     is large.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Lu2024,

title = {On the scaling and critical layer in a turbulent boundary layer over a compliant surface},

author = {Yuhui Lu and Tianrui Xiang and Tamer A. Zaki and Joseph Katz},

doi = {10.1017/jfm.2024.11},

issn = {1469-7645},

year  = {2024},

date = {2024-01-31},

journal = {J. Fluid Mech.},

volume = {980},

publisher = {Cambridge University Press (CUP)},

abstract = {Simultaneous time-resolved measurements of wall deformation and the 3-D velocity field in boundary layers over a compliant surface are performed by integrating Mach Zehnder interferometry with tomographic particle tracking velocimetry. The pressure is calculated by spatially integrating the material acceleration. Combining data obtained from several references, trends of the deformation r.m.s. scaled by the compliant wall thickness collapse when plotted vs pressure fluctuations scaled by the material shear modulus. For the present data, at all Reynolds numbers, the deformation waves travel at 53% of the free-stream velocity and have a preferred wavelength of three times the thickness. The latter is consistent with theoretical models. Adopting insight derived from atmospheric wind–wave interactions, the pressure–deformation correlations peak at or slightly above the ‘critical layer’, where the mean flow speed is equal to the surface wave speed. This layer is located within the log layer, and when expressed using inner variables, increases in elevation with increasing Reynolds number. For the entire region below the critical layer, wavenumber–frequency spectra of pressure and vertical velocity fluctuations indicate that the turbulence is phase locked and travels with the deformation, even for deformation amplitudes much smaller than a wall unit. In contrast, above the critical layer, the turbulence is advected at the local mean streamwise velocity, and its correlation with the deformation decays rapidly. These findings indicate that the height of the zone dominated by flow-deformation interactions is determined by the surface wave speed, and its variations are caused by deformation-induced modifications to the mean velocity profile.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yamani_etal_2023,

title = {Spatiotemporal signatures of elastoinertial turbulence in viscoelastic planar jets},

author = {Sami Yamani and Yashasvi Raj and Tamer A. Zaki and Gareth H. McKinley and Irmgard Bischofberger},

url = {https://link.aps.org/doi/10.1103/PhysRevFluids.8.064610},

doi = {10.1103/PhysRevFluids.8.064610},

year  = {2023},

date = {2023-06-01},

journal = {Phys. Rev. Fluids},

volume = {8},

issue = {6},

pages = {064610},

publisher = {American Physical Society},

keywords = {Jet, Polymer, Viscoelastic},

pubstate = {published},

tppubtype = {article}

}

@article{jahanbakhshi_zaki_2023,

title = {Optimal two-dimensional roughness for transition delay in high-speed boundary layer},

author = {Reza Jahanbakhshi and Tamer A. Zaki},

doi = {10.1017/jfm.2023.523},

year  = {2023},

date = {2023-01-01},

journal = {Journal of Fluid Mechanics},

volume = {968},

pages = {A24},

keywords = {Boundary layers, High-speed boundary layers, Hypersonic, Roughness, Stability, Transition},

pubstate = {published},

tppubtype = {article}

}

@article{cheung_zaki_2023,

title = {An eigen-representation of the Navier–Stokes equations},

author = {Lawrence C. Cheung and Tamer A. Zaki},

url = {https://www.sciencedirect.com/science/article/pii/S0377042722005192},

doi = {https://doi.org/10.1016/j.cam.2022.114921},

issn = {0377-0427},

year  = {2023},

date = {2023-01-01},

journal = {Journal of Computational and Applied Mathematics},

volume = {423},

pages = {114921},

abstract = {In this paper we demonstrate that the incompressible Navier–Stokes equations can be formulated as a system of quadratic polynomial equations with a regular, tractable structure. This is first shown to be possible by using the combination matrix of Cheung and Zaki (2014) on the time-harmonic Navier–Stokes with periodic boundaries. We also show that the initial value problem can be rewritten in a similar fashion using the Laguerre polynomial basis and the appropriate version of the combination matrix. The solution to both these formulations, when using a finite number of terms in the series expansion, can be found through the null space of the Macaulay matrix and leads to an eigenvalue problem. We also provide two examples which illustrate the methods discussed in this work. The approach is demonstrated on a nonlinear, univariate model differential equation, and also on the two dimensional Taylor Green vortex problem.},

keywords = {Algebraic geometry, Eigenvalue problem, Navier–Stokes},

pubstate = {published},

tppubtype = {article}

}

@article{clarkdileoni_etal_2023,

title = {Neural operator prediction of linear instability waves in high-speed boundary layers},

author = {Patricio Clark Di Leoni and Lu Lu and Charles Meneveau and George Em Karniadakis and Tamer A. Zaki},

url = {https://www.sciencedirect.com/science/article/pii/S0021999122008567},

doi = {https://doi.org/10.1016/j.jcp.2022.111793},

issn = {0021-9991},

year  = {2023},

date = {2023-01-01},

journal = {Journal of Computational Physics},

volume = {474},

pages = {111793},

abstract = {We investigate if neural operators can predict the linear evolution of instability waves in high-speed boundary layers. To this end, we extend the design of the DeepOnet to ensure accurate and robust predictions, and also to perform data assimilation. In particular, we train DeepONet to take as inputs an upstream disturbance and a downstream location of interest, and to provide as output the perturbation field downstream in the boundary layer. DeepONet thus approximates the linearized and parabolized Navier-Stokes operator for this flow. For successful application to the high-speed boundary layer problem, we add sample weighting and Fourier input features to the regular DeepONet formulation. Once trained, the DeepOnet can perform fast and accurate predictions of the downstream disturbances within the range of training frequencies (inside the distribution). In addition, we show that DeepONet can solve the inverse problem, where downstream wall measurements are adopted as input, and a trained network can predict the upstream disturbances that led to these observations. This capability, along with the forward predictions, allows us to perform a full data assimilation cycle efficiently: starting from wall-pressure data, we predict the upstream disturbance using the inverse DeepONet and its evolution using the forward DeepONet. Finally, we introduce three new metrics to benchmark the training, evaluation and break-even cost of neural operators.},

keywords = {Deep operator networks, DeepONet, High-speed boundary layers, Instability waves, Machine Learning, Neural operators},

pubstate = {published},

tppubtype = {article}

}

@article{yang_etal_2023,

title = {The three-dimensional elastodynamic solution for dislocation plasticity and its implementation in discrete dislocation dynamics simulations},

author = {Junjie Yang and Ali Rida and Yejun Gu and Daniel Magagnosc and Tamer A. Zaki and Jaafar A. El-Awady},

url = {https://www.sciencedirect.com/science/article/pii/S1359645423002768},

doi = {https://doi.org/10.1016/j.actamat.2023.118945},

issn = {1359-6454},

year  = {2023},

date = {2023-01-01},

journal = {Acta Materialia},

volume = {253},

pages = {118945},

abstract = {An analytical solution for the elastodynamic displacement field of non-uniformly moving Volterra dislocations is derived using the Green's function approach. The elastodynamics strain and stress fields can then be evaluated by numerically differentiating the displacement field. Qualitative comparisons are made with molecular dynamic simulations, and the analytical solution is shown to capture the same features. The plane waves that emanate from, and are parallel to, the slip plane during the instantaneous injection process of edge or screw dislocations are captured by the analytical solution. This was not captured by previously proposed elastodynamic solutions. A computationally efficient swept-area-tracking algorithm is then developed and implemented into three-dimensional discrete dislocation dynamics simulations to compute the elastodynamic field induced by dislocation movements and interactions. This approach provides a way forward for modeling deformation of materials under shock loading or quantifying the dynamics effects that dominate during dislocation avalanches during deformation of metals.},

keywords = {Boundary value problems, Dislocation dynamics, Elastodynamic solution, Stress waves},

pubstate = {published},

tppubtype = {article}

}

@article{hao_etal_2023,

title = {Instability-wave prediction in hypersonic boundary layers with physics-informed neural operators},

author = {Yue Hao and Patricio Clark Di Leoni and Olaf Marxen and Charles Meneveau and George Em Karniadakis and Tamer A. Zaki},

url = {https://www.sciencedirect.com/science/article/pii/S1877750323001801},

doi = {https://doi.org/10.1016/j.jocs.2023.102120},

issn = {1877-7503},

year  = {2023},

date = {2023-01-01},

journal = {Journal of Computational Science},

volume = {73},

pages = {102120},

abstract = {Fast and accurate prediction of the nonlinear evolution of instability waves in high-speed boundary layers requires specialized numerical algorithms, and augmenting limited observation in this extreme flow regime is challenging. The deep operator networks (DeepONet) has been shown to be an effective tool for providing accurate and fast physics-informed predictions. DeepONet is trained to map an incoming perturbation to the associated downstream flow field within the nonlinear flow regime. The training is performed using high-fidelity data from direct numerical simulations of the compressible Navier–Stokes equations, when the gas can be approximated as calorically perfect and when chemical non-equilibrium effects must be computed. The performance and requirements of training the DeepONet in each case are evaluated. In addition, we show that informing the training of the DeepONet with the continuity equation improves the accuracy of the results, especially in absence of sufficient training data. Success of the physics-informed DeepONet to predict missing fields depends on the observables. Specifically, prediction of a unique solution depends on the available measurements. These results are a promising step towards applications of neural operator networks to more complex high-speed flow configurations and to data assimilation.},

keywords = {Deep operator networks, DeepONet, High-speed boundary layers, Hypersonics, Machine Learning, Non-equilibrium chemical reaction},

pubstate = {published},

tppubtype = {article}

}

@article{du_etal_2023,

title = {State estimation in minimal turbulent channel flow: A comparative study of 4DVar and PINN},

author = {Yifan Du and Mengze Wang and Tamer A. Zaki},

url = {https://www.sciencedirect.com/science/article/pii/S0142727X22001412},

doi = {https://doi.org/10.1016/j.ijheatfluidflow.2022.109073},

issn = {0142-727X},

year  = {2023},

date = {2023-01-01},

journal = {International Journal of Heat and Fluid Flow},

volume = {99},

pages = {109073},

abstract = {The state of turbulent, minimal-channel flow is estimated from spatio-temporal sparse observations of the velocity, using both a physics-informed neural network (PINN) and adjoint-variational data assimilation (4DVar). The performance of PINN is assessed against the benchmark results from 4DVar. The PINN is efficient to implement, takes advantage of automatic differentiation to evaluate the governing equations, and does not require the development of an adjoint model. In addition, the flow evolution is expressed in terms of the network parameters which have a far smaller dimension than the predicted trajectory in state space or even just the initial condition of the flow. Provided adequate observations, network architecture and training, the PINN can yield satisfactory estimates of the flow field, both for the missing velocity data and the entirely unobserved pressure field. However, accuracy depends on the network architecture, and the dependence is not known a priori. In comparison to 4DVar estimation which becomes progressively more accurate over the observation horizon, the PINN predictions are generally less accurate and maintain the same level of errors throughout the assimilation time window. Another notable distinction is the capacity to accurately forecast the flow evolution: while the 4DVar prediction depart from the true flow state gradually and according to the Lyapunov exponent, the PINN is entirely inaccurate immediately beyond the training time horizon unless re-trained. Most importantly, while 4DVar satisfies the discrete form of the governing equations point-wise to machine precision, in PINN the equations are only satisfied in an L2 sense.},

keywords = {4DVar, Adjoint variational method, Data assimilation, Physics informed neural networks, PINN, State estimation, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{clarkdileoni_etal_2023bb,

title = {Reconstructing turbulent velocity and pressure fields from under-resolved noisy particle tracks using physics-informed neural networks},

author = {Patricio Clark Di Leoni and Karuna Agarwal and Tamer A. Zaki and Charles Meneveau and Joseph Katz},

url = {https://doi.org/10.1007/s00348-023-03629-4},

doi = {10.1007/s00348-023-03629-4},

isbn = {1432-1114},

year  = {2023},

date = {2023-01-01},

journal = {Experiments in Fluids},

volume = {64},

number = {5},

pages = {95},

abstract = {Volume-resolving imaging techniques are rapidly advancing progress in experimental fluid mechanics. However, reconstructing the full and structured Eulerian velocity and pressure fields from under-resolved and noisy particle tracks obtained experimentally remains a significant challenge. We adopt and characterize a method based on Physics-Informed Neural Networks (PINNs). In this approach, the network is regularized by the Navier–Stokes equations to interpolate the velocity data and simultaneously determine the pressure field. We compare this approach to the state-of-the-art Constrained Cost Minimization method Agarwal et al. (2021). Using data from direct numerical simulations and various types of synthetically generated particle tracks, we show that PINNs are able to accurately reconstruct both velocity and pressure even in regions with low particle density and small accelerations. We analyze both the root-mean-square error of the reconstructions as well their energy spectra. PINNs are also robust against increasing the distance between particles and the noise in the measurements, when studied under synthetic and experimental conditions. Both the synthetic and experimental datasets used correspond to moderate Reynolds number flows.},

keywords = {Data assimilation, Machine Learning, PINN},

pubstate = {published},

tppubtype = {article}

}

@article{fowler_zaki_meneveau_2023,

title = {A multi-time-scale wall model for large-eddy simulations and applications to non-equilibrium channel flows},

author = {Mitchell Fowler and Tamer A. Zaki and Charles Meneveau},

doi = {10.1017/jfm.2023.585},

year  = {2023},

date = {2023-01-01},

journal = {Journal of Fluid Mechanics},

volume = {974},

pages = {A51},

publisher = {Cambridge University Press},

keywords = {Channel, Turbulence, Wall modeling},

pubstate = {published},

tppubtype = {article}

}

@article{yao_etal_2023,

title = {Entropy and fluctuation relations in isotropic turbulence},

author = {Hanxun Yao and Tamer A. Zaki and Charles Meneveau},

doi = {10.1017/jfm.2023.808},

year  = {2023},

date = {2023-01-01},

journal = {Journal of Fluid Mechanics},

volume = {973},

pages = {R6},

publisher = {Cambridge University Press},

keywords = {Entropy, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{buchta_jfm2022,

title = {Assimilation of wall-pressure measurements in high-speed flow over a cone},

author = {David A. Buchta and Stuart J. Laurence and Tamer A. Zaki},

doi = {10.1017/jfm.2022.668},

year  = {2022},

date = {2022-01-01},

journal = {Journal of Fluid Mechanics},

volume = {947},

pages = {R2},

publisher = {Cambridge University Press},

keywords = {Boundary layers, Data assimilation, Hypersonic, Stability, Transition},

pubstate = {published},

tppubtype = {article}

}

@article{wang_Stochastic_jfm2022,

title = {Origin of enhanced skin friction at the onset of boundary-layer transition},

author = {Mengze Wang and Gregory L. Eyink and Tamer A. Zaki},

doi = {10.1017/jfm.2022.296},

year  = {2022},

date = {2022-01-01},

journal = {Journal of Fluid Mechanics},

volume = {941},

pages = {A32},

publisher = {Cambridge University Press},

keywords = {Channel, Data assimilation, Drag, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{esteghamatian_jfm2022,

title = {Spatiotemporal characterization of turbulent channel flow with a hyperelastic compliant wall},

author = {Amir Esteghamatian and Joseph Katz and Tamer A. Zaki},

doi = {10.1017/jfm.2022.354},

year  = {2022},

date = {2022-01-01},

journal = {Journal of Fluid Mechanics},

volume = {942},

pages = {A35},

publisher = {Cambridge University Press},

keywords = {Channel, Compliant walls, Turbulence, Viscoelastic},

pubstate = {published},

tppubtype = {article}

}

@article{wang_Synch_jfm2022,

title = {Synchronization of turbulence in channel flow},

author = {Mengze Wang and Tamer A. Zaki},

doi = {10.1017/jfm.2022.397},

year  = {2022},

date = {2022-01-01},

journal = {Journal of Fluid Mechanics},

volume = {943},

pages = {A4},

publisher = {Cambridge University Press},

keywords = {Channel, Data assimilation, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{wang_Hesisan_jfm2022,

title = {What is observable from wall data in turbulent channel flow?},

author = {Qi Wang and Mengze Wang and Tamer A. Zaki},

doi = {10.1017/jfm.2022.295},

year  = {2022},

date = {2022-01-01},

journal = {Journal of Fluid Mechanics},

volume = {941},

pages = {A48},

publisher = {Cambridge University Press},

keywords = {Channel, Data assimilation, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{fowler_jfm2022,

title = {A Lagrangian relaxation towards equilibrium wall model for large eddy simulation},

author = {Mitchell Fowler and Tamer A. Zaki and Charles Meneveau},

doi = {10.1017/jfm.2021.1156},

year  = {2022},

date = {2022-01-01},

journal = {Journal of Fluid Mechanics},

volume = {934},

pages = {A44},

publisher = {Cambridge University Press},

keywords = {Channel, LES, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{page_zaki_2022,

title = {Vorticity amplification in wavy viscoelastic channel flow},

author = {Jacob Page and Tamer A. Zaki},

doi = {10.1017/jfm.2022.757},

year  = {2022},

date = {2022-01-01},

journal = {Journal of Fluid Mechanics},

volume = {949},

pages = {A14},

publisher = {Cambridge University Press},

keywords = {Channel, Polymer, Roughness, Stability, Viscoelastic, Wavy},

pubstate = {published},

tppubtype = {article}

}

@article{mons_prf2021,

title = {Ensemble-variational assimilation of statistical data in large-eddy simulation},

author = {Vincent Mons and Yifan Du and Tamer A. Zaki},

url = {https://link.aps.org/doi/10.1103/PhysRevFluids.6.104607},

doi = {10.1103/PhysRevFluids.6.104607},

year  = {2021},

date = {2021-10-01},

journal = {Phys. Rev. Fluids},

volume = {6},

issue = {10},

pages = {104607},

publisher = {American Physical Society},

keywords = {Channel, Data assimilation, Ensemble Variational Methods, EnVar, LES, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{Du_pre2021,

title = {Evolutional deep neural network},

author = {Yifan Du and Tamer A. Zaki},

url = {https://link.aps.org/doi/10.1103/PhysRevE.104.045303},

doi = {10.1103/PhysRevE.104.045303},

year  = {2021},

date = {2021-10-01},

journal = {Phys. Rev. E},

volume = {104},

issue = {4},

pages = {045303},

publisher = {American Physical Society},

keywords = {Deep learning, Machine Learning, Neural Networks},

pubstate = {published},

tppubtype = {article}

}

@article{zaki_prf2021,

title = {From limited observations to the state of turbulence: Fundamental difficulties of flow reconstruction},

author = {Tamer A. Zaki and Mengze Wang},

url = {https://link.aps.org/doi/10.1103/PhysRevFluids.6.100501},

doi = {10.1103/PhysRevFluids.6.100501},

year  = {2021},

date = {2021-10-01},

journal = {Phys. Rev. Fluids},

volume = {6},

issue = {10},

pages = {100501},

publisher = {American Physical Society},

keywords = {Data assimilation, Ensemble Variational Methods, EnVar, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{sami_prl2021,

title = {Spectral Universality of Elastoinertial Turbulence},

author = {Sami Yamani and Bavand Keshavarz and Yashasvi Raj and Tamer A. Zaki and Gareth H. McKinley and Irmgard Bischofberger},

url = {https://link.aps.org/doi/10.1103/PhysRevLett.127.074501},

doi = {10.1103/PhysRevLett.127.074501},

year  = {2021},

date = {2021-08-01},

journal = {Phys. Rev. Lett.},

volume = {127},

issue = {7},

pages = {074501},

publisher = {American Physical Society},

keywords = {Jet, Polymer, Viscoelastic},

pubstate = {published},

tppubtype = {article}

}

@article{ghanash_prf2021,

title = {Large eddy simulation of transitional channel flow using a machine learning classifier to distinguish laminar and turbulent regions},

author = {Ghanesh Narasimhan and Charles Meneveau and Tamer A. Zaki},

url = {https://link.aps.org/doi/10.1103/PhysRevFluids.6.074608},

doi = {10.1103/PhysRevFluids.6.074608},

year  = {2021},

date = {2021-07-01},

journal = {Phys. Rev. Fluids},

volume = {6},

issue = {7},

pages = {074608},

publisher = {American Physical Society},

keywords = {Channel, LES, Transition},

pubstate = {published},

tppubtype = {article}

}

@article{mao_jcp2021,

title = {DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators},

author = {Zhiping Mao and Lu Lu and Olaf Marxen and Tamer A. Zaki and George Em Karniadakis},

url = {https://www.sciencedirect.com/science/article/pii/S0021999121005933},

doi = {https://doi.org/10.1016/j.jcp.2021.110698},

issn = {0021-9991},

year  = {2021},

date = {2021-01-01},

journal = {Journal of Computational Physics},

volume = {447},

pages = {110698},

keywords = {Chemically reacting flow, Data assimilation, Deep learning, DeepONet, Hypersonic, Operator approximation},

pubstate = {published},

tppubtype = {article}

}

@article{buchta_jfm2021,

title = {Observation-infused simulations of high-speed boundary-layer transition},

author = {David A. Buchta and Tamer A. Zaki},

doi = {10.1017/jfm.2021.172},

year  = {2021},

date = {2021-01-01},

journal = {Journal of Fluid Mechanics},

volume = {916},

pages = {A44},

publisher = {Cambridge University Press},

keywords = {Data assimilation, Ensemble Variational Methods, EnVar, Hypersonic},

pubstate = {published},

tppubtype = {article}

}

@article{jahanbakhshi_jfm2021,

title = {Optimal heat flux for delaying transition to turbulence in a high-speed boundary layer},

author = {Reza Jahanbakhshi and Tamer A. Zaki},

doi = {10.1017/jfm.2021.210},

year  = {2021},

date = {2021-01-01},

journal = {Journal of Fluid Mechanics},

volume = {916},

pages = {A46},

publisher = {Cambridge University Press},

keywords = {Hypersonic, Roughness, Transition},

pubstate = {published},

tppubtype = {article}

}

@article{wang_jfm2021,

title = {State estimation in turbulent channel flow from limited observations},

author = {Mengze Wang and Tamer A. Zaki},

doi = {10.1017/jfm.2021.268},

year  = {2021},

date = {2021-01-01},

journal = {Journal of Fluid Mechanics},

volume = {917},

pages = {A9},

publisher = {Cambridge University Press},

keywords = {Adjoint, Channel, Data assimilation, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{esteghamatian_jfm2021,

title = {The dynamics of settling particles in vertical channel flows: gravity, lift and particle clusters},

author = {Amir Esteghamatian and Tamer A. Zaki},

doi = {10.1017/jfm.2021.304},

year  = {2021},

date = {2021-01-01},

journal = {Journal of Fluid Mechanics},

volume = {918},

pages = {A33},

publisher = {Cambridge University Press},

keywords = {Channel, Particles, Turbulence, Viscoelastic},

pubstate = {published},

tppubtype = {article}

}

@article{clark_di_leoni_jfm2021,

title = {Two-point stress--strain-rate correlation structure and non-local eddy viscosity in turbulent flows},

author = {Patricio Clark Di Leoni and Tamer A. Zaki and George Karniadakis and Charles Meneveau},

doi = {10.1017/jfm.2020.977},

year  = {2021},

date = {2021-01-01},

journal = {Journal of Fluid Mechanics},

volume = {914},

pages = {A6},

publisher = {Cambridge University Press},

keywords = {LES, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{cai_jcp2021,

title = {DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks},

author = {Shengze Cai and Zhicheng Wang and Lu Lu and Tamer A. Zaki and George Em Karniadakis},

url = {https://www.sciencedirect.com/science/article/pii/S0021999121001911},

doi = {https://doi.org/10.1016/j.jcp.2021.110296},

issn = {0021-9991},

year  = {2021},

date = {2021-01-01},

journal = {Journal of Computational Physics},

volume = {436},

pages = {110296},

keywords = {Data assimilation, Deep learning, DeepONet, Multiscale modeling, Mutiphysics, Operator approximation},

pubstate = {published},

tppubtype = {article}

}

@article{you_jfm2021,

title = {Concave-wall turbulent boundary layers without and with free-stream turbulence},

author = {Jiho You and David A. Buchta and Tamer A. Zaki},

doi = {10.1017/jfm.2021.12},

year  = {2021},

date = {2021-01-01},

journal = {Journal of Fluid Mechanics},

volume = {915},

pages = {A4},

publisher = {Cambridge University Press},

keywords = {Boundary layers, Curvature, Freestream Turbulence, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{wu_prf2020,

title = {Data compression for turbulence databases using spatiotemporal subsampling and local resimulation},

author = {Zhao Wu and Tamer A Zaki and Charles Meneveau},

url = {https://link.aps.org/doi/10.1103/PhysRevFluids.5.064607},

doi = {10.1103/PhysRevFluids.5.064607},

year  = {2020},

date = {2020-06-01},

journal = {Phys. Rev. Fluids},

volume = {5},

pages = {064607},

publisher = {American Physical Society},

keywords = {Data assimilation},

pubstate = {published},

tppubtype = {article}

}

@article{eyink_gupta_zaki_2020b,

title = {Stochastic Lagrangian dynamics of vorticity. Part 2. Application to near-wall channel-flow turbulence},

author = {Gregory L Eyink and Akshat Gupta and Tamer A Zaki},

doi = {10.1017/jfm.2020.492},

year  = {2020},

date = {2020-01-01},

journal = {Journal of Fluid Mechanics},

volume = {901},

pages = {A3},

publisher = {Cambridge University Press},

keywords = {Channel, Drag, Navier-Stokes, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{esteghamatian_zaki_2020,

title = {Viscoelasticity and the dynamics of concentrated particle suspension in channel flow},

author = {Amir Esteghamatian and Tamer A Zaki},

doi = {10.1017/jfm.2020.525},

year  = {2020},

date = {2020-01-01},

journal = {Journal of Fluid Mechanics},

volume = {901},

pages = {A25},

publisher = {Cambridge University Press},

keywords = {Channel, Drag, Particles, Polymer, Viscoelastic},

pubstate = {published},

tppubtype = {article}

}

@article{eyink_gupta_zaki_2020,

title = {Stochastic Lagrangian dynamics of vorticity. Part 1. General theory for viscous, incompressible fluids},

author = {Gregory L Eyink and Akshat Gupta and Tamer A Zaki},

doi = {10.1017/jfm.2020.491},

year  = {2020},

date = {2020-01-01},

journal = {Journal of Fluid Mechanics},

volume = {901},

pages = {A2},

publisher = {Cambridge University Press},

keywords = {Channel, Drag, Navier-Stokes, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{Wu3461,

title = {High-Reynolds-number fractal signature of nascent turbulence during transition},

author = {Zhao Wu and Tamer A Zaki and Charles Meneveau},

url = {https://www.pnas.org/content/117/7/3461},

doi = {10.1073/pnas.1916636117},

issn = {0027-8424},

year  = {2020},

date = {2020-01-01},

journal = {Proceedings of the National Academy of Sciences},

volume = {117},

number = {7},

pages = {3461--3468},

publisher = {National Academy of Sciences},

keywords = {Bypass, Conditional Sampling, Freestream Turbulence, Machine Learning, Spots, T/NT interface, Transition, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{you_ftc2020,

title = {Turbulent Heat-Transfer Enhancement in Boundary Layers Exposed to Free-Stream Turbulence},

author = {Jiho You and Tamer A Zaki},

url = {https://doi.org/10.1007/s10494-019-00071-7},

doi = {10.1007/s10494-019-00071-7},

isbn = {1573-1987},

year  = {2020},

date = {2020-01-01},

journal = {Flow, Turbulence and Combustion},

abstract = {Direct numerical simulations (DNS) are performed to study the effect of free-stream vortical forcing on a thermal turbulent boundary layer. In presence of external perturbations, the heat-transfer rate from the wall is increased relative to the unforced case. An explanation is provided, and starts from the free-stream forcing which enhances the Reynolds stresses inside the boundary layer, and in particular the wall-normal component. As a result, the wall-normal heat flux is also increased, which has the dual effect of distorting the base temperature profile and enhancing the production of scalar variance; both contribute to the increase in the wall heat-transfer rate. In addition, the flow sustains higher thermal fluctuations, even though the free-stream forcing is only vortical, and not thermal. These changes are accompanied by modification of the spectra of the thermal field in the outer region of the boundary layer, where large-scale thermal structures are formed in response to the large-scale velocity motions. In the near-wall region, the thermal structures are modulated by the outer hydrodynamic field and are strengthened relative to the unforced flow.},

keywords = {Scalar, T/NT interface, Turbulence, Very-large-scale Motion},

pubstate = {published},

tppubtype = {article}

}

@article{hameduddin_jfm2019,

title = {Perturbative expansions of the conformation tensor in viscoelastic flows},

author = {I Hameduddin and D Gayme and T A Zaki},

url = {https://engineering.jhu.edu/zaki/wp-content/uploads/2018/12/Hameduddin_JFM_2019.pdf},

year  = {2019},

date = {2019-01-01},

journal = {Journal of Fluid Mechanics},

volume = {858},

pages = {377-406},

keywords = {Channel, Polymer, Shear, Viscoelastic},

pubstate = {published},

tppubtype = {article}

}

@article{Wang_jcp2019,

title = {Discrete adjoint of fractional-step incompressible Navier-Stokes solver in curvilinear coordinates and application to data assimilation},

author = {Mengze Wang and Qi Wang and Tamer A Zaki},

url = {http://www.sciencedirect.com/science/article/pii/S0021999119304735},

doi = {https://doi.org/10.1016/j.jcp.2019.06.065},

issn = {0021-9991},

year  = {2019},

date = {2019-01-01},

journal = {Journal of Computational Physics},

volume = {396},

pages = {427 - 450},

abstract = {The discrete adjoint of an incompressible Navier-Stokes algorithm in generalized coordinates is derived and applied to estimate the states of saturated and turbulent circular Couette flows. The forward Navier-Stokes model is based on the fractional-step algorithm in curvilinear coordinates on a structured grid [1], which has been widely adopted in direct numerical simulations of transitional and turbulent flows. The discrete adjoint equations adopt the same stencil and temporal scheme as the forward discretization, and expressions are derived that relate the discrete adjoint variables to their continuous counterpart. The key ingredients of the forward algorithm can be retained in the adjoint, including the computation of the cell geometry, the approximate factorization method, and the parallelization strategy. The accuracy, efficiency, and stability of the adjoint solver are also commensurate with the forward model. In addition, a novel symmetric projector is proposed to guarantee that the outcome of the adjoint algorithm is divergence free. The implementation of the algorithm in double precision satisfies the forward-adjoint relation up to eight significant figures, and further validation is performed using circular Couette flow. The forward and adjoint growth rates of instability modes from linear theory are accurately reproduced. In addition, an adjoint-variational data-assimilation algorithm (4DVar) is adopted to reconstruct the initial condition of circular Couette flows from limited measurements, obtained from an independent simulation. When the flow is comprised of saturated wavy vortices, wall measurements are sufficient to reconstruct an initial condition that latches onto the target state after a short time. For the more challenging turbulent case, coarse-grained velocity data are used to estimate the initial condition.},

keywords = {Data assimilation, Discrete adjoint, Fraction-step algorithm, Generalized coordinates, Navier-Stokes, Taylor-Couette flow},

pubstate = {published},

tppubtype = {article}

}

@article{jahanbakhshi_jfm2019,

title = {Nonlinearly most dangerous disturbance for high-speed boundary-layer transition},

author = {Reza Jahanbakhshi and Tamer A Zaki},

doi = {10.1017/jfm.2019.527},

year  = {2019},

date = {2019-01-01},

journal = {Journal of Fluid Mechanics},

volume = {876},

pages = {87--121},

publisher = {Cambridge University Press},

keywords = {Hypersonic, Optimization, Transition},

pubstate = {published},

tppubtype = {article}

}

@article{esteghamatian_jfm2019,

title = {Dilute suspension of neutrally buoyant particles in viscoelastic turbulent channel flow},

author = {Amir Esteghamatian and Tamer A Zaki},

doi = {10.1017/jfm.2019.483},

year  = {2019},

date = {2019-01-01},

journal = {Journal of Fluid Mechanics},

volume = {875},

pages = {286--320},

publisher = {Cambridge University Press},

keywords = {Channel, Drag, Particles, Polymer, Viscoelastic},

pubstate = {published},

tppubtype = {article}

}

@article{wang_jfm2019,

title = {Spatial reconstruction of steady scalar sources from remote measurements in turbulent flow},

author = {Qi Wang and Yosuke Hasegawa and Tamer A Zaki},

doi = {10.1017/jfm.2019.241},

year  = {2019},

date = {2019-01-01},

journal = {Journal of Fluid Mechanics},

volume = {870},

pages = {316--352},

publisher = {Cambridge University Press},

keywords = {Adjoint, Channel, Optimization, Scalar, Scalar dispersion},

pubstate = {published},

tppubtype = {article}

}

@article{wu_prf2019,

title = {Application of a self-organizing map to identify the turbulent-boundary-layer interface in a transitional flow},

author = {Zhao Wu and Jin Lee and Charles Meneveau and Tamer Zaki},

url = {https://link.aps.org/doi/10.1103/PhysRevFluids.4.023902},

doi = {10.1103/PhysRevFluids.4.023902},

year  = {2019},

date = {2019-01-01},

journal = {Phys. Rev. Fluids},

volume = {4},

pages = {023902},

publisher = {American Physical Society},

keywords = {Bypass, Machine Learning, Spots, T/NT interface, Transition, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{park_jfm2019,

title = {Sensitivity of high-speed boundary-layer stability to base-flow distortion},

author = {J Park and T A Zaki},

url = {https://engineering.jhu.edu/zaki/wp-content/uploads/2018/12/Park_JFM_2019.pdf},

year  = {2019},

date = {2019-01-01},

journal = {Journal of Fluid Mechanics},

volume = {859},

pages = {476-515},

keywords = {Adjoint, Hypersonic, Instability, Sensitivity, Stability, Transition},

pubstate = {published},

tppubtype = {article}

}